Known paper cups are made from paper segments wound using a folding mandrel into a frustum shape. By shaping of a top curl on the top edge of the frustum-shaped cup sleeve and by inserting a bottom into the cup sleeve, a paper cup for receiving liquids is provided. If hot beverages are to be received, the paper cup can be additionally provided with an insulating outer envelope. During shaping of the top curl and also during connection of the bottom to the cup sleeve at an all-round bottom edge, the paper material of the cup sleeve must be curled or folded round by at least 180°. To do so, the paper material must be compressed in the area of the bottom edge, and partly stretched and partly compressed in the area of the top curl. Compressing leads to an excess of paper material and hence to a more or less rippled surface. This can be accepted on an inside of the bottom edge, but a rippled surface cannot be accepted at the top curl. As a result, numerous measures must be taken in the area of the top curl in order to make a top curl with a smooth surface. The compressing or stretching of the paper material during curling or folding round is all the greater as the cone angle of the cup sleeve increases. Using the example of the top curl, the upper rim of the cup sleeve in the case of a cylindrical tube is stretched during curling, as soon as it has been curled by 360° and hence substantially is back in its initial position, but there is no substantial material stretching or material compression. This is not the case with frustum-shaped sleeves, since the upper rim of the cup sleeve is moved during provision of the top curl into a position in which a smaller diameter is obtained in comparison with the original diameter of the upper rim. After a curling process of the upper rim by 360° too, the paper material of the upper rim must therefore be able to sustain a permanent material compression without creasing. The greater the cone angle of the cup sleeve, the greater this diameter difference is and the greater is the tendency during creation of the top curl and during creation of the bottom edge to crease. For this reason, conventional paper cups are made with a cone angle of the cup sleeve of 9° at most.